Subdividing Geometry Images in Graphics Hardware

ABSTRACT

A system may include a graphics memory, a data bus, a processor, and a vertex shader. The data bus may be operatively connected to the graphics memory. The processor may send vertex data to the graphics memory via the data bus. The vertex shader may read the vertex data from the graphics memory and may subdivide the vertex data into subdivided vertex data. The vertex shader may also write the subdivided vertex data to the graphics memory.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/926,875, filed on Aug. 26, 2004.

BACKGROUND

Implementations of the claimed invention generally may relate toprocessing graphical images and, more particularly, to processinggraphical images using geometry images.

FIG. 1 is a flow chart illustrating typical graphics processing 100.Geometry representing graphical images may be submitted to a graphicspipeline [act 110]. Such geometry typically may include triangles, butmay include quadrilaterals or any other type of geometry. Vertex shadersmay then process the geometry, performing such processing astransforming and lighting each polygon, determining colors for vertices,determining normals if necessary, etc. [act 120]. Vertex shaderstypically include hardware that implements an instruction set to operateon data associated with vertices. Such data may include the vertexposition, vertex normal, and per vertex texture coordinates. Thesevalues may also be used later by the shading hardware to interpolateacross a polygon to create a shaded image.

Next, the polygons may be clipped to the screen in appropriate positions[act 130]. Pixel shaders may then shade each polygon [act 140]. Pixelshaders typically include hardware that execute a set of instructions oneach fragment as it passes through the graphics pipeline before beingrendered to the screen. Pixel and vertex shaders may have identical ordifferent instruction sets. Additionally, the instruction sets theyexecute may be different than the instructions exposed to a programmer.

After shading, if a particular pixel is in front of any previouslyrendered pixels, it may be written to the frame buffer [act 150]. Insome graphical engines, alpha blending may occur. Alpha blending is amechanism to facilitate the implementation of partially transparentobjects and typically may be realized through an additional channel tothe color channels used in a traditional three-dimensional (3D) graphicspipeline.

Recently, a technique of representing the surface geometry of graphicalimages has been proposed that may have certain advantages. Such atechnique may remesh an arbitrary graphical surface onto a completelyregular structure called a “geometry image.” The geometry image maycapture the surface geometry of a graphical image as a two-dimensional(2D) array of quantized points. Surface signals, such as normals and/orcolors, may be stored in similar 2D images using the same surfaceparameterization as the geometry image. Further discussion of geometryimages may be found in, for example, Xianfeng Gu et al., “GeometryImages,” SIGGRAPH 2002 Proceedings, pp. 355-361; and F. Losasso et al.,“Smooth Geometry Images,” Eurographics 2003, pp. 138-145 and 273. Tobetter understand what a geometry image is and how it may represent a 3Dgraphical object, a brief explanation will be provided.

FIG. 2 illustrates formation of a geometry image 250 from a 3D model 210(see, e.g., Hughes Hoppe, “Irregular To Completely Regular Meshing InComputer Graphics,” International Meshing Roundtable 2002, September2002). 3D model 210 may be conceptualized as a two-dimensional (2D)shape bent and warped in 3D space to form a 3D mesh. Model 210 mayinclude such a mesh of geometric shapes (e.g., triangles,quadrilaterals, etc.) that are defined by vertices and edges between thevertices. The vertices in model 210 may have associated spatialcoordinate values in a 3D coordinate system (e.g., [x, y, z]coordinates).

3D Model 210 may be cut along its edges to form a different (e.g.,non-rabbit-shaped) 2D shape. Cut 220 illustrates one such cut. Thisdifferent shape may be warped or parameterized using known techniques toform a regular shape 230. Regular shape 230 may include connectedvertices from model 210 (e.g., illustrated as triangles), with the cut220 being located at the outer edge(s) of shape 230. Thus, regular shape230 retains both the [x, y, z] position values of the vertices in model210, as well as the connection relationships between these vertices. Itshould be noted that although regular shape 230 is illustrated as asquare, other types of regular shapes (e.g., circles, etc.) may also beused.

The polygons in regular shape 230 may be regularly sampled to generatesampled shape 240. Each sampled point in sampled shape 240 may be a newvertex that both retains a positional value (e.g., an [x, y, z]coordinate) and that is implicitly connected to other vertices insampled image 240. That is, vertices in sampled image 240 may beconnected be edges to other vertices to their top, bottom, left, andright sides by virtue of the regular sampling of regular shape 230.

Sampled image 240 may be converted into a red/green/blue (RGB) (or anyother color space) color image by mapping the three-channel [x, y, z]coordinates of the vertices in sampled image 240 to the three-channelRGB space, [r, g, b] coordinates, to produce geometry image 250. Eachpixel in geometry image 250 may represent a sampled vertex in model 210,with the red, green, and blue values of the pixel representing the [x,y, z] spatial position of the sampled vertex. The neighbor vertices ofthe corresponding sampled vertex in model 210 are determined by theneighboring pixels to a given pixel in geometry image 250. In otherwords, the neighbor vertices of model 210 are known by the neighborpixels in geometry image 250, and the positional values of thesevertices are known by the color values for pixels in geometry image 250.

Although geometry image 250 has been explained with regard to positionalinformation, geometry images 250 may be generated for any informationassociated with the vertices of model 210. For example, normals, whichare [x, y, z] vectors that point into space, may also be represented bya geometry image 250. Also, color values and/or texture coordinates mayalso be represented by geometry images 250. Representing models asimages may allow one to use existing image processing algorithms, suchas image compression algorithms.

Although it is possible to compress geometry images, such geometryimages, even if compressed, may in some instances be sent to a graphicsprocessor over a data bus. In some cases, the bandwidth of the data busmay limit the resolution and/or visual fidelity able to be displayed bythe graphics processor from the geometry images.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate one or more implementationsconsistent with the principles of the invention and, together with thedescription, explain such implementations. The drawings are notnecessarily to scale, the emphasis instead being placed uponillustrating the principles of the invention. In the drawings,

FIG. 1 is flow chart illustrating typical graphics processing;

FIG. 2 illustrates formation of a geometry image;

FIG. 3 illustrates an example system; and

FIG. 4 is a flow chart illustrating a process of subdividing graphicsdata.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawings.The same reference numbers may be used in different drawings to identifythe same or similar elements. In the following description, for purposesof explanation and not limitation, specific details are set forth suchas particular structures, architectures, interfaces, techniques, etc. inorder to provide a thorough understanding of the various aspects of theclaimed invention. However, it will be apparent to those skilled in theart having the benefit of the present disclosure that the variousaspects of the invention claimed may be practiced in other examples thatdepart from these specific details. In certain instances, descriptionsof well known devices, circuits, and methods are omitted so as not toobscure the description of the present invention with unnecessarydetail.

FIG. 3 illustrates an example system 300. System 300 may include a mainmemory 310, a processor 320, a data bus 330, a graphics memory 340, oneor more vertex shaders 350, one or more pixel shaders 360, and a framebuffer 370. In some implementations, one or more of elements 340-370 maybe included in a physically distinct graphics card that is connected toprocessor 320 via data bus 330. In some implementations, elements340-370 may be located on a common circuit board (e.g., a motherboard,daughter card, etc.) with elements 310 and 320. In some implementations,one or more of elements 350 and 360 may be part of one portion (e.g., acore) of a device, and processor 320 may be include in another portion(e.g., another core) of the same device.

Main memory 310 may include a storage device to store geometry images.Main memory 310 may include a random access memory (RAM) device, such asa dynamic RAM (DRAM), double data rate RAM (DDR RAM), etc. Main memory310 may store pre-computed geometry images and/or graphical data fromwhich to compute geometry images.

Processor 320 may include a general-purpose processor, aspecific-purpose processor, and/or logic configured for a specificpurpose. Processor 320 may be arranged to distribute geometry imagesfrom main memory 310 to graphics memory 340 via data bus 330. Processor320 may send the geometry images via data bus 330 under control of aprogram, such as a rendering, game, graphical creation, or other type ofgraphics-related program. In some implementations, processor 320 maycompute the geometry images from other information in main memory 310and store the geometry images in main memory 310. In someimplementations, processor 320 may compress the geometry images (e.g.,via JPEG 2000 or another lossless scheme) before transmission via databus 330.

Data bus 330 may connect processor 320 to graphics memory 340. Data bus330 may use a typical interconnect protocol, or may use a customcommunication protocol. Data bus 330 may have an associated bandwidththat defines a maximum amount of data that it can transfer in a giventime. In some implementations, the bandwidth of data bus 330 may limitthe performance of other portions of system 300 (e.g., shaders 350and/or 360). In some implementations, the bandwidth of data bus 330 maynot limit the overall performance of system 300.

Graphics memory 340 may include a storage device to store geometryimages. Graphics memory 340 may include a random access memory (RAM)device, such as a dynamic RAM (DRAM), double data rate RAM (DDR RAM),etc. Graphics memory 340 may receive and store geometry images fromprocessor 320 and vertex shaders 350. In addition to storing geometryimages via write operations, graphics memory 340 may provide suchgeometry images to vertex shaders 350 and pixel shaders 360 via readoperations. For example, graphics memory 340 may store various“per-vertex” data associated with the geometry images. Such vertex datamay include one or more of vertex positions, texture coordinates, colorcoordinates, or normal vectors.

Vertex shaders 350 may be arranged to read the vertex data from graphicsmemory 340 and to subdivide the vertex data to generatehigher-resolution vertex data. Vertex shaders 350 may have a parallelarchitecture, and may have a larger instruction set than, for example,pixel shaders 360. Vertex shaders 350 may use various vertex generationprograms and subdivision schemes to increase the resolution of thevertex data, as will be described further herein. Vertex shaders 350 mayalso write the higher-resolution vertex data to graphics memory 340.

Because of a relatively high-bandwidth access to graphics memory 340,vertex shaders 350 may write a relatively large amount ofhigher-resolution vertex data to graphics memory 340. Typicalsubdivision schemes may increase the amount of data in a geometry imageby a factor of four. Vertex shaders 350 may be arranged to perform oneor more levels of subdivision for a given geometry image, andonce-subdivided vertex data stored in graphics memory 340, for example,may be used by vertex shaders 350 to generate a second level ofsubdivided data (e.g., at a higher/finer resolution) for storage ingraphics memory 340.

Pixel shaders 360 may be arranged to read the subdivided vertex datafrom graphics memory 340 and prepare it for display. Pixel shaders 360may have a higher bandwidth connection to graphics memory 340 than, forexample, vertex shaders 350, and pixel shaders 360 may be able morelimited in number of instructions and instruction set than vertexshaders 350. For example, pixel shaders 360 may be arranged to read thenew, higher-resolution geometry images from graphics memory 340,rasterize the images, and send the rasterized pixel data to frame buffer370. In some implementations, pixel shaders 360 may rasterize the newgeometry images using the lower-resolution geometry images fromprocessor 320 (which may remain in graphics memory 340) as displayprimitives.

Frame buffer 370 may be arranged to receive pixel data from pixelshaders 360 and buffer it, if necessary, prior to display. Frame buffer370 may also output data to a display or display interface, possiblyunder control of a graphics processor (not shown).

FIG. 4 is a flow chart illustrating a process 400 of subdividinggraphics data. Although process 400 may be described with regard tosystem 300 for ease of explanation, the claimed invention is notnecessarily limited in this regard.

Processing may begin with processor 320 obtaining textures, geometryimages, and any other associated values for vertex positions in an image[act 410]. In some implementations, processor 320 may compute thevalues, and in some implementations processor 320 may read the valuesfrom main memory 310. In addition to obtaining a geometry image,processor 320 may also create one or more of a texture coordinate mapand a color coordinate map. Detailed procedures for creating geometryimages (e.g., cutting a mesh along edge paths and parameterizing theresulting chart into a square) may be found in, for example, Xianfeng Guet al., “Geometry Images,” SIGGRAPH 2002 Proceedings, pp. 355-361. Suchtexture map, geometry image, and/or color map may be implemented asarrays having specified widths and heights.

Texture, color, and/or normal maps may be created in the same fashion asthe vertex map in FIG. 2. For textures, tu and tv may be stored in thered and green channels respectively. Likewise, for color r, g, and bvalues may be stored into the r, g, and b values for the texture map.Because textures are normally just arrays of colors, both color andtexture maps use r, g, and b. Finally, x, y, and z values of the normalsmay be stored into the r, g, and b channels of the texture map. Itshould be noted that such mapping need not be restricted to a 2Dstructure, such as an image. Rather, the techniques described herein maysupport textures, normals, and colors by consuming any number ofchannels that are mapped into r, g, b, and (if necessary) alpha. If morethan 4 channels of vertex-related information or data are desired,additional texture maps may be used for this information. Thus, thetechnique described with regard to FIG. 2 may be used with somewhatarbitrary and/or complex vertex data.

Also in act 410, processor 320 may create placeholder arrays for thetextures, geometry images and colors when subdivided one or more times.Such placeholder arrays may be sent over data bus 330 in shorthand formusing minimal bandwidth to reserve space in graphics memory 340 for thesubdivided textures, geometry images, etc. In some implementations, theplaceholder arrays may be generated locally by vertex shaders 350 inresponse to a command from processor 320. In any event, the placeholderarrays may be initialized to zero and stored in graphics memory 340.

Processing may continue with processor 320 sending the textures,geometry images, and any other values (e.g., color coordinates and/ornormal vectors) to graphics memory 340 via data bus 330 [act 420]. Insome implementations, processor 320 may submit the textures, geometryimages, and any other values to a graphics application programminginterface (API), which may handle transporting the textures and geometryimages to graphics memory 340. In some implementations, the textures,geometry images, etc. may be compressed (e.g., via a lossless schemesuch as JPEG 2000) before transmission over data bus 330.

Vertex shaders 350 may read the stored textures, geometry images, andany other values (collectively “vertex data”) from graphics memory 340and may subdivide the vertex data [act 430]. As previously mentioned,subdivision of a two-dimensional image (e.g., a geometry image) mayincrease the resolution of the image by roughly four times. In someimplementations, vertex shaders 350 may implement the subdivision usingthe Catmull-Clark technique outlined in Ed Catmull and Jim Clark,“Recursively Generated B-Spline Surfaces on Arbitrary TopologicalMeshes,” Computer Aided Geometric Design, Vol. 10, Nov. 6, 1978.

Other subdivision techniques may be employed, however, by vertex shaders350. In some implementations, vertex shaders 350 may subdivide thevertex data using the butterfly technique outlined in “SubdividingReality: Employing Subdivision Surfaces for Real Time ScalablePhotorealism,” by Stephen Junkins, Game Developers Conferenceproceedings, 2000. In some implementations, vertex shaders 350 maysubdivide the vertex data using the loop technique outlined in C. T.Loop, “Smooth Subdivision Surfaces Based on Triangles,” M. S. Thesis,Department of Mathematics, University of Utah, August, 1987. In someimplementations, vertex shaders 350 may subdivide the vertex data usingthe Doo-Sabin technique outlined in D. Doo and M. Sabin, “Behavior ofRecursive Division Surfaces Near Extraordinary Points,” Computer AidedDesign, Vol. 10, Nov. 6, 1978.

Vertex shaders 350 may write the subdivided, output vertex data tographics memory 340 [act 440]. In some implementations, vertex shaders350 overwrite one or more placeholder arrays in graphics memory 340 withthe output vertex data. In some implementations, vertex shaders 350 maycreate new structures in graphics memory 340 for the output vertex dataas needed.

Depending on a number of levels of desired subdivision, vertex shaders350 may repeat acts 430 and 440 one or more times, as illustrated by thedashed arrow in FIG. 4. For example, if more than one subdivisionoperation is desired (e.g., to produce a greater resolution), vertexshaders 350 may read and further subdivide once-subdivided (ortwice-subdivided if repeating act 430 a second time) output vertex datastored in graphics memory 340 in a previous act 440. Because subdivisionmay depend on vertex data at the immediately preceding resolution (e.g.,the output of the prior subdivision), in some implementations vertexshaders 350 may overwrite and/or delete vertex data of a higherresolution to free space in graphics memory 340. For example, whenperforming a second (or higher) level of subdivision, the originalvertex data sent from processor 320 may be overwritten and/or deleted.

Other techniques may also be employed when subdividing to save space ingraphics memory 340 and/or other resources of system 300. For example,space in graphics memory 340 may be saved by not subdividing texture,normal and/or color coordinates as fully as, for example, the associatedgeometry images. In such a case, pixel shaders 360 may just reference alower level of subdivision (e.g., only once subdivided data for a twiceor more subdivided resolution) and divide by 4 for each lookup. As oneexample, if generating and/or storing a 256.times.256 normal map alongwith a corresponding 256.times.256 geometry image is not desirable, anormal map from the 64.times.64 level of resolution may be used by pixelshaders 360 instead. For an entry at index (32,32) in the positionarray, position (8,8) in the 64.times.64 normal map may be referenced bypixel shaders 360 during their processing. Thus, pixel shaders 360 mayuse one or more maps of a lower resolution (e.g., a normal map) whenformatting other vertex data (e.g., a geometry image or other structure)that has been subdivided to a higher resolution by vertex shaders 350.

In some implementations, an appropriate normal may be computed, and thenthe closest normal may be looked up in the old normal map. The resultingnormal data may be stored in a normal map of any size. Other techniquesmay be used to avoid, for a given resolution, fully subdividing allgraphical data in graphics memory 340.

Subdivision may not be desired in some areas (e.g., areas within ageometry image). For those areas, the existing geometry image, normalimage, and/or texture maps may be left alone. For the other areas thatare desirable to subdivide, a subdivision scheme may be employed (e.g.,Catmull-Clark). For borders between the two regions (e.g., subdividedand not) some vertex information may be duplicated.

Another technique to save space in graphics memory 340 may be tocompress the data stored therein (e.g., the original vertex data and/orthe subdivided vertex data) via a lossless compression scheme. One suchscheme that may be suitable for compressing, for example, subdividedgeometry images may be JPEG 2000, which may achieve compression ratiosof about 2.5 to 1. Data compression may be used instead of, or inaddition to, other techniques for reducing the amount of data stored ingraphics memory 340.

Processing may continue with pixel shaders 360 preparing the subdividedvertex data stored in graphics memory 340 for display [act 450]. Pixelshaders 360 may rasterize and/or otherwise format the stored vertex data(e.g., geometry images, color maps, etc.) for display. In someimplementations, pixel shaders 360 may prepare the subdivided vertexdata using one or more lower resolution sets of vertex data (e.g.,original geometry images) as display primitives. Although not explicitlyshown in FIG. 4, the formatted graphical images may then be displayedfrom frame buffer 370.

The above-described system and scheme of subdividing vertex data viavertex shaders 350 may in some implementations increase a visualfidelity/resolution of displayed data for a given bandwidth of datacarried by data bus 330. For example, vertex data that uses most orsubstantially all of the bandwidth of data bus 330 may be subdivided byvertex shaders 350 to increase display resolution over what mayotherwise be possible due to the bandwidth of data bus 330. In someimplementations, such a subdivision scheme may facilitate producing agiven visual fidelity/resolution using less bandwidth of data bus 330than if subdivision was not performed. For example, the displayresolution may remain the same as that in the case where no subdivisionwas performed, but subdivision allows the former case to usesubstantially less bandwidth of data bus 330 for the same resolution.

To further aid in understanding the above-described system 300 andprocess 400, an example will be presented. In this example, processor320 may create or read from main memory 320 in act 410 three n.times.n(n being an integer, such as 8, 16, 32, etc.) arrays, G0, T0, and C0. G0may be a geometry image. T0 may be a texture coordinate map, with eachposition containing corresponding texture coordinates. C0 may be a colorcoordinate cap, with each position containing corresponding red, green,and blue color values. G0, T0, and C0 may be at an original resolution(e.g., 8.times.8, 16.times.16, etc.).

Also in act 410, for each level of subdivision desired (e.g., twolevels), processor 320 and/or vertex shaders 350 may create aplaceholder array/map for each of G0, T0, and C0 at a respectivesubdivided resolution. For a first level of subdivision, G1, T1, and C1may be created with a size/resolution of 4*n.times.4*n, becausesubdivision may increase size/resolution of an array/image by a factorof four. For a second level of subdivision, G2, T2, and C2 may becreated with a size/resolution of 4*4*n.times.4*4*n (i.e.,16n.times.16n). For convenience, G1, T1, C1, G2, T2, and C2 may beinitialized to zero.

In act 420, processor 320 may send structures G0, T0, C0, G1, T1, C1,G2, T2, and C2 to graphics memory 340 via data bus 330. In someimplementations, such operation may be performed using a graphics API.This operation may initialize space in graphics memory 340 to be filledin later by vertex shader 350.

Vertex shaders 350 may then subdivide G0, T0, and C0 to generate firstsubdivided vertex data G1, T1, and C1 in act 430. For example, if theparticular subdivision scheme employed is Catmull-Clark subdivisionscheme, new face points for a face may be calculated by averaging oldpoints defining the face. New edge points may be calculated by averagingmidpoints of old edges with the average of the two new face points ofthe faces sharing an edge. New vertex points may be calculated byaveraging Q/n+(2*R)/n+(S*(n−3))/n, where Q equals the average of newface points of all faces adjacent to old vertex point; R equals theaverage of midpoints of all old edges incident on old vertex point, andS is the old vertex point. Other subdivision schemes than Catmull-Clarkmay be used in some implementations.

As each set of points in G1, T1, and C1 is created, vertex shaders 350may store the values in the corresponding placeholder structures ingraphics memory 340 in act 440. When the first subdivision issufficiently complete, vertex shaders 350 may further subdivide G1, T1,and C1 to generate second subdivided vertex data G2, T2, and C2 in act430. Vertex shaders 350 may store the further subdivided values in thecorresponding placeholder structures G2, T2, and C2 in graphics memory340 in act 440. As previously explained, G1, T1, or C1 may not undergo asecond level of subdivision in some implementations. Pixel shaders 360may read the finally-subdivided vertex data (e.g., G2, T2, and C2 if allhave been twice-subdivided) from graphics memory 340 and prepare it fordisplay via frame buffer 370. In implementations where G0, T0, and C0are not all subdivided twice, pixel shaders 360 may prepare G2 and oneor more less-subdivided structures, such as T1 and/or C1, for display.

Although the above illustrative example includes a specificimplementation, the claimed invention is not necessarily limitedthereto. For example, the initial vertex data may include differentgraphical data than G0, T0, and C0, such as normal data. The number ofsubdivisions performed by vertex shaders 350 may be less than or greaterthan two. Similarly, a different subdivision scheme than Catmull-Clarkmay be used in some implementations.

The foregoing description of one or more implementations providesillustration and description, but is not intended to be exhaustive or tolimit the scope of the invention to the precise form disclosed.Modifications and variations are possible in light of the aboveteachings or may be acquired from practice of various implementations ofthe invention.

For example, although the subdivision scheme herein has been describedwith regard to vertex shaders 350, in some implementations othergraphics hardware may be used to implement subdivision. Such otherhardware (e.g., other types of shaders, etc.) may be suitable if it hasthe ability to read vertex data from and write subdivided vertex data tographics memory 340.

Further, the subdivision scheme described herein may be performed on anas-needed basis (e.g., substantially in real time) by vertex shaders 350in some implementations, and it may be pre-computed by vertex shaders350 in some implementations. Also, in some implementations, vertexshaders 350 may send the subdivided vertex data directly to pixelshaders 360, rather than first writing it to graphics memory 340.

Moreover, the acts in FIG. 4 need not be implemented in the order shown;nor do all of the acts necessarily need to be performed. Also, thoseacts that are not dependent on other acts may be performed in parallelwith the other acts. Further, at least some of the acts in this figuremay be implemented as instructions, or groups of instructions,implemented in a machine-readable medium.

No element, act, or instruction used in the description of the presentapplication should be construed as critical or essential to theinvention unless explicitly described as such. Also, as used herein, thearticle “a” is intended to include one or more items. Variations andmodifications may be made to the above-described implementation(s) ofthe claimed invention without departing substantially from the spiritand principles of the invention. All such modifications and variationsare intended to be included herein within the scope of this disclosureand protected by the following claims.

1. A system, comprising: a memory to store first geometry images havinga first resolution; vertex shaders to subdivide the first geometryimages into second geometry images having a second resolution higherthan the first resolution and to store the second geometry images in thememory; and pixel shaders to prepare the second geometry images fordisplay.
 2. The system of claim 1, further comprising: a frame buffer tobuffer and output data from the pixel shaders.
 3. The system of claim 1,further comprising: a processor to obtain the first geometry images andsend the first geometry images to the memory.
 4. The system of claim 3,further comprising: another memory to store the first geometry imagesfor access by the processor.
 5. The system of claim 1, wherein the pixelshaders rasterize the second geometry images.
 6. The system of claim 1,wherein the second resolution is about four times greater than the firstresolution.
 7. A method, comprising: obtaining first geometry images ofa first size; storing the first geometry images; subdividing the firstgeometry images into second geometry images of a second size that islarger than the first size; and storing the second geometry images. 8.The method of claim 7, wherein the obtaining includes: computing thefirst geometry images.
 9. The method of claim 7, wherein the obtainingincludes: reading the first geometry images from a memory.
 10. Themethod of claim 7, wherein the second size is about four times greaterthan the first size.
 11. The method of claim 7, further comprising:subdividing the second geometry images into third geometry images of athird size that is larger than the second size; and storing the thirdgeometry images.
 12. The method of claim 7, further comprising:transmitting the first geometry images via a data bus before the storingthe first geometry images.
 13. The method of claim 7, furthercomprising: rasterizing the second geometry images.